In conventional logging systems used in the exploration and production of hydrocarbons from subterranean formations, the distances between the electrodes or antennas are usually great enough that the rock volume involved in a measurement may include several thin beds having different lithological characteristics and, therefore different resistivity. Such layering can arise from the existence of clay layers or from compacted sand beds of differing grain sizes.
When individual layers are not resolved by a logging tool, the tool responds to the formation as if it were a macroscopically anisotropic formation. It holds true for thinly laminated sand/shale sequences.
If a rock sample is cut from the anisotropic formation, the resistivity of the sample measured with current flowing parallel to the bedding plane is called the transversal or horizontal resistivity. The resistivity measured with the current flowing perpendicular to the bedding plane is called the longitudinal or vertical resistivity.
One of the generally accepted approaches to measure the resistivity anisotropy of layered rock sample consists of following steps. A cube is cut from the layered rock sample. Then measurement of the resistivity of the cube in the three orthogonal directions is performed. The two resistivities measured for current flow parallel to bedding are longitudinal resistivities, ρt and they should be fairly similar. The resistivity measured with current across bedding is the transverse resistivity, ρn. The ratio Λ=√{square root over (ρn/ρt)} is called the coefficient of anisotropy.
Typically, a core sample is cylindrical with flat end faces. Both two- and four-electrode measurement configurations are known which allow the effective determination of resistivity of isotropic core samples.
In the two-electrode case current is injected through two cap electrodes at the ends. With two-electrode design the current and potential electrodes are combined. The rock-electrode couplings constitute the principal disadvantages of two-electrode measurements, if badly designed. The contact resistance decreases with increasing pressure, so the contacts must be put under enough pressure to make the contact resistance a small fraction of the rock resistance.
Advantages of two-electrode arrays include the resistivity measurement of entire sample. This is considered desirable, since the porosity and water saturation are also generally measured on the entire sample.
In the four-electrode case, current is similarly injected through two cap electrodes at the ends. However, a four-electrode arrangement incorporates two additional ring electrodes. These measuring electrodes (metal rings) are placed along the core length. The advantage of the four-electrode setup is that it is not sensitive to the contact resistance. A disadvantage, however, is that the voltage is measured over a shorter distance and the result can be sensitive to small inhomogeneities in the core.
Both two- and four-electrode measurement configurations have a similar dominant characteristic: they are symmetric relative to the major axis of the cylindrical core sample. Neither arrangement has heretofore been shown to be effective in resistivity measurements on anisotropic samples.